Tým vyřešil hádanku, aniž by odemkl truhlu.

Because Czech verb agreement follows the grammatical subject, not the real-world number of people inside the group. Tým is a singular noun, so the verb is singular too: tým vyřešil.

Also, tým is grammatically masculine, which is why the past form ends in -l. If the subject were truly plural, for example členové týmu (the team members), then the verb would be plural: Členové týmu vyřešili hádanku.

Aniž by means something like without doing or without having done. In this sentence, it introduces a subordinate clause explaining what did not happen while the main action happened:

Tým vyřešil hádanku, aniž by odemkl truhlu.
= The team solved the riddle without unlocking the chest.

English often uses without + -ing, but Czech commonly uses aniž by + verb form instead.

Because aniž by is a standard Czech pattern. The particle by is the same one used in the conditional, and after aniž it helps form this without doing construction.

So learners should usually think of aniž by as one unit of meaning, rather than trying to translate each word separately every time.

After aniž by, Czech normally does not use the infinitive. It uses a finite-style verb form with by:

• aniž by odemkl
• not aniž by odemknout

So even though English says without unlocking, Czech uses a different structure. The form odemkl here is the l-participle form used with by in this construction.

Because the Czech form used here is the same l-participle that also appears in the past tense. Compare:

• odemkl = part of he/it unlocked
• by odemkl = would unlock / used in structures like aniž by odemkl

So in this sentence, odemkl is not simply an ordinary past tense meaning unlocked. It is part of the aniž by construction.

Because the subject is understood to be the same as in the main clause: tým. Czech often leaves the subject unstated when it is clear from context.

So this sentence effectively means:

Tým vyřešil hádanku, aniž by [tým] odemkl truhlu.

Repeating tým would usually be unnecessary unless you wanted special emphasis or needed to avoid ambiguity.

Both are in the accusative singular, because they are direct objects of the verbs:

• vyřešit hádanku = to solve a riddle
• odemknout truhlu = to unlock a chest

Their nominative forms are:

• hádanka → hádanku
• truhla → truhlu

This is a very common feminine singular pattern in Czech: nominative -a often becomes accusative -u.

Because the sentence refers to whole, completed events.

• vyřešit is perfective: to solve completely
• odemknout is perfective: to unlock

So vyřešil hádanku means the riddle was successfully solved, and aniž by odemkl truhlu means the completed act of unlocking did not happen.

If you used imperfective verbs, the meaning would shift. For example, aniž by odemykal truhlu would sound more like without even unlocking/trying to unlock it as a process, which is a different nuance.

Because aniž by odemkl truhlu is a subordinate clause, and Czech normally separates subordinate clauses with a comma.

So the comma is standard and expected here:

Tým vyřešil hádanku, aniž by odemkl truhlu.

Not necessarily in an absolute sense. What it clearly says is that the team solved the riddle without unlocking the chest as part of that action or beforehand.

The usual implication is that unlocking the chest was not needed for solving the riddle. But the sentence does not by itself rule out the possibility that the chest was unlocked later.

Yes. A few alternatives are possible, though they are not all identical in style.

For example:

• Tým vyřešil hádanku bez toho, aby odemkl truhlu.
• Tým vyřešil hádanku bez odemčení truhly.

The original aniž by version is very natural and elegant. The bez toho, aby version is also common but slightly heavier. The bez odemčení truhly version turns the action into a noun phrase, which can sound a bit more compact or formal.